We are talking about the battle rounds, right? If so then yes, I'm sure--or at least that's how it's presented to the audience. I suppose there could be behind the scenes pressure applied by producers etc. but the stated rules are that the coaches make the choice of which singers are paired up, as well as which song they sing and which singer wins the battle.

Wikipedia says:

In the second stage, called the battle phase, coaches have two of their team members battle against each other directly by singing the same song together, with the coach choosing which team member to advance from each of individual "battles" into the first live round.